Pure, high quality essential oils will never go rancid. However, over the course of years, a process called oxidation will occur. This simply means the introduction of oxygen into the chemical composition of the oil. However, it can change the therapeutic properties of oils and can also make them irritate skin and mucous membranes. Citrus oils are the fastest to oxidize and will do so in 3-5 years. Some oils will oxidize in 20 years (or more). Read more about how to store essential oils in order to prevent oxidation as much as possible.
Oils that are not true essential oils and/or oils that have been mixed with a carrier oil will not follow this rule. Any time an oil has been mixed with something (whether by you or by the company you bought them from), the shelf life of the mixture is the shelf life of the carrier oil. The carrier oil will likely start to smell rancid around the time of its expiration date and then you will want to discard that.